1. a total of three freshmen, five sophomores, 3 juniors and 4 seniors are eligible for a $3000 scholarship, a $2000 scholarship and a $1000 scholarship. in how many different ways can these scholarships be awarded if at least two of them must go to senior

So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.

Step-by-step explanation:

In this problem, there are three scolarships.

The first step to solve this question is ensuring that two seniors receive their scolarships.

There are 4 seniors, and we must guarantee two scolarships to them. If senior A receives the first scolarship and senior B the second, or A receives the second and B the first, it is the same thing, so the order does not interfere with the problem. It means it is a combination problem.

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The formula for the number of possible combinations of r objects from a set of n objects is:

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So, for the senior scolarships, we have combinations of two(scolarships) objects from a set of four(seniors) objects: So

There are 12 ways to ensure two of those scolarships to those seniors.

The are 13 students vying for the last scolarship(hree freshmen, five sophomores, 3 juniors and two seniors that didn't get the first two).

So those scholarships can be awarded in 13*12 = 156 different ways ensuring that at least two of them go to seniors.

i dont know

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: